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Are Logical Laws Descriptive or Prescriptive?

A conversation taking place in another thread is really interesting to me, because it centers on a phenomenon I’ve come across few times when talking about logical laws and so on.

The phenomenon is something like this:

In my experience, atheists or agnostics tend to hold that “logical laws” are abstracts invented by humans to express brute facts that we observe in and about nature. That is, they are tools we have invented to give an abstract assignment to things we observe in the world. Yes, the words we use to describe what we see are in fact properties of nature, but the words describe nature. They don’t prescribe it. That is, I don’t see that logical laws are things that exist apart from nature; I don’t see that they are ‘pre-existing’ or ‘external’ rules against which nature was designed.

On the other hand, theists tend to hold that logical laws are things that transcend nature; that they are things to which nature conforms, rather than human-invented expressions that help us describe and communicate the things we observe in nature. I get the sense that they see these rules as things that are discovered – not about nature – but rather, about reality itself. They view them as (perhaps) a sort of existing, metaphysical ‘template’ against which all possible words can be created.

[NOTE: It is not my intention to incorrectly describe anyone’s views, general or otherwise. Indeed, the whole point of this thread is to discuss these things and learn. So please bear in mind that the views I’ve described above are my best guesses relative to the state of mind I was in when I created the thread.]

What I’d like to have happen in this thread is a dialog about this topic. I’m not married to any particular position, and I don’t want this to turn into a point/counterpoint antagonistic sort of contest. But for the sake of discussion I have to admit that what I described as the atheist/agnostic view is the one that most resonates with me.

So, to start it off, I’ll describe some reasons why I think I prefer the former over the latter, and I hope to hear some of what you guys think.

When I think about a logical law, I try to think about how it corresponds with nature. For example, the law of identity says that a thing is itself and nothing else, and so when I think about that, it seems to correspond with the brute fact that I am not my keyboard and it is not me, etc. But when I think about these “rules”, I DO see them as describing fundamental aspects of nature. But I DON’T see that they transcend it. They ARE nature itself, and it seems to me that if nature were different, the rules would be different.

Bear in mind that this is a space where I go very much by how I “feel” about these things. That is, when we’re talking about brute fact of nature, the conversation tends lay at the very base of what it means to “know” something, so I don’t feel like I’m in a position where I can be especially persuasive (unlike a conversation where, say, I had to show that I was born in the United States or something). As it relates to empirical data, we’re at the very boundary of knowing and assuming. I think this is important because, when people are talking at this level concerning things they know, there’s a good opportunity to gain some insight into how others see the world, and what aspects of nature appeal to them and why.

Re: Are Logical Laws Descriptive or Prescriptive?

When I think about a logical law, I try to think about how it corresponds with nature. For example, the law of identity says that a thing is itself and nothing else, and so when I think about that, it seems to correspond with the brute fact that I am not my keyboard and it is not me, etc. But when I think about these “rules”, I DO see them as describing fundamental aspects of nature. But I DON’T see that they transcend it. They ARE nature itself, and it seems to me that if nature were different, the rules would be different.

But laws go beyond describing merely what we have observed; rather, they purport to describe a general principle or requirement. E.g. if we've seen only houses built with four walls, we shouldn't reason that there's a physical or logical law such that houses must have four walls. Nor should we imagine that there are millions of separate laws of gravity for each type of object in our worldview--a law of gravity for round objects, a law of gravity for blue objects, etc.

I'm not sure what feature of nature you could have observed that would lead you to think, say, "Every locally-compact Hausdorff space is completely regular," or more to the point, "" (axiom 5 of S5 in modal logic)

If I am capable of grasping God objectively, I do not believe, but precisely because I cannot do this I must believe. - Soren Kierkegaard**** you, I won't do what you tell me

Re: Are Logical Laws Descriptive or Prescriptive?

Originally Posted by Dionysus

In my experience, atheists or agnostics tend to hold that “logical laws” are abstracts invented by humans to express brute facts that we observe in and about nature. That is, they are tools we have invented to give an abstract assignment to things we observe in the world. Yes, the words we use to describe what we see are in fact properties of nature, but the words describe nature. They don’t prescribe it. That is, I don’t see that logical laws are things that exist apart from nature; I don’t see that they are ‘pre-existing’ or ‘external’ rules against which nature was designed.

On the other hand, theists tend to hold that logical laws are things that transcend nature; that they are things to which nature conforms, rather than human-invented expressions that help us describe and communicate the things we observe in nature. I get the sense that they see these rules as things that are discovered – not about nature – but rather, about reality itself. They view them as (perhaps) a sort of existing, metaphysical ‘template’ against which all possible words can be created.

I think the salient issues are highlighted by a historical example, but first let me make a few cursory comments. Firstly, I would commit myself to the idea that there are "Nomological laws" (Laws of Nature), as it does seem that Nature conforms to laws, in the sense that there exist objects in reality and these objects obey rules. We have no idea what they are; we do have a good degree of certainty that we know limiting cases of these laws, and we know about the objects which are apparent to exist in these regimes. But I don't think that the laws of logic themselves are "transcendent", per se. I think that they are products of the human mind, and statements about how we categorize reality. The best historical example of this is how the notion of a "particle" has evolved.

If you asked a philosopher or a physicist 150 years ago what a particle was, you'd have gotten a very precise, very simple definition involving some notion of an point-size object possessing a precise position and momentum at a given time, whose position and momentum evolve in time subject to the laws of dynamics. Under this definition, a particle cannot be in more than one place at once, a particle's position and momentum are completely deterministic, they cannot have angular momentum associated to them, and so on. However, it was well-known following Young's experiment and the Stern-Gerlach experiment that our notion of a particle \was "wrong."

Notice that no one said "Nature has broken the laws of logic! A particle cannot not be probabilistic, cannot have a spin, and cannot have an uncertain amount of momentum and position." The obvious conclusion is that our definition of a particle was flawed, not that particles in Nature are flawed. So you throw out your old definitions of particles (The Newtonian Mechanics picture) and you replace it with a new picture (The Quantum Mechanics picture). That, also, wasn't good enough when you included relativity, and so you have to throw out that picture and you have to use the Quantum Field Theory picture, where particles are very abstract objects, indeed. But I think this illuminates the point: There's no experiment that can show that the universe is "inconsistent." Every time something that violates our paradigm is confirmed (i.e. is repeated in experiments), we toss aside the paradigm and create a new one that can account for the previous inconsistency.

As near as I can tell, the best anyone could do if the universe was appearing to violate "the laws of logic" is to say that "the universe doesn't obey laws, and thus the universe is chaotic" (i.e. we cannot predict what will happen in the future based upon the present). But I can't think of any way for the universe to literally "violate the laws of logic."

An expanded (though still brief) statement of my epistemological framework:

So I think that to my mind I have my own epistemological framework for how I think about the world, and I have thought about this issue to some degree. My primary claim would be that there's two different forms existing (existing as a thought in the mind, existing as an object in reality), and that we can thoroughly explore them. I would place statements and properties about ideas (that which exists in minds) under the Hume's category of "relations of ideas" (analytic statements), and statements and properties regarding objects existing in reality as "facts of the matter" (synthetic statements). Relations of ideas are really statements about how humans think about and, more importantly, categorize reality, and we can proceed deductively based off of definitions. However, none of this tells us how reality "is." We have to use experience and observation in order to gain knowledge of this, but it's always incomplete because the limited nature of our precision in measuring things, the theoretical inputs we place into each experiment, and the fact that we can only make probabilistic statements about reality.

Originally Posted by CliveStaples

But laws go beyond describing merely what we have observed; rather, they purport to describe a general principle or requirement. E.g. if we've seen only houses built with four walls, we shouldn't reason that there's a physical or logical law such that houses must have four walls. Nor should we imagine that there are millions of separate laws of gravity for each type of object in our worldview--a law of gravity for round objects, a law of gravity for blue objects, etc.

I'm not sure what feature of nature you could have observed that would lead you to think, say, "Every locally-compact Hausdorff space is completely regular," or more to the point, "" (axiom 5 of S5 in modal logic)

It depends on what you mean by the words that you're using here. You've written down two laws (propositions) that are analytic statements. In other words, they're statements that are true by definition, not statements that are true because they comport with what we observe or experience about reality. In fact, in the case of the Axiom S5, it's not true for any reason other than that you've asserted it to be true. You can build modal logics with or without the Axiom S5. Likewise, the proposition that "Every locally-compact Hausdorff space is completely regular" is not true or false because our experiences or observations of locally-compact Hausdorff spaces leads us to believe it is so. We can reflect on the well-formed definitions and rules of inference, and then we infer that the proposition is necessarily true and thus forms a theorem.

A more relevant example would be a physical law, but as I've shown above, the idea that descriptions of physical objects must conform to some kind of tautologically true properties (whatever that could even mean) is simply not cut and dry.

"Those who can make you believe absurdities, can make you commit atrocities." --Voltaire